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Radians Appendix Add in library

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40 Download5 Pages 1,225 Words

Question:

Describe about the Radians Appendix?
 
 

Answer:

We have taken around 640 points for calculating the ordinates separated by 0.01 radians. Some of the points are shown in the following table, while rest can be found in the appendix.
 
 

V1

V2

R

0

121.2436

-100

21.24356

0.01

121.9375

-99.995

21.94248

0.02

122.6192

-99.98

22.63921

0.03

123.2887

-99.955

23.33368

0.04

123.9458

-99.92

24.02582

0.05

124.5906

-99.875

24.71555

0.06

125.2229

-99.8201

25.40281

0.07

125.8426

-99.7551

26.08753

0.08

126.4498

-99.6802

26.76964

0.09

127.0443

-99.5953

27.44908

0.1

127.6262

-99.5004

28.12577

0.11

128.1953

-99.3956

28.79964

0.12

128.7515

-99.2809

29.47064

 

The graph obtained for the signals and their resultant are shown in the following figure:

The magnitude of the resultant can be calculated as :

The magnitude of the phase is given as:

Using the trapezoidal rule and taking 10 point intervals we have the following values:

 

Interval length(h=0.3)

Velocity

 

1

0.3

17.11

8.555

2

0.6

15.04

15.04

3

0.9

12.79

12.79

4

1.2

10.36

10.36

5

1.5

7.75

7.75

6

1.8

4.96

4.96

7

2.1

1.99

1.99

8

2.4

-1.16

-1.16

9

2.7

-4.49

-4.49

10

3

-8

-4

   

Sum

51.795

   

Total distance(sum*h)

15.5385

 

Average Acceleration:

Using the midpoint ordinate rule and taking 10 point intervals we have the following values:

 

Interval length(h=0.3)

Mid points

 

1

0.3

0.45

16.0975

2

0.6

0.75

13.9375

3

0.9

1.05

11.5975

4

1.2

1.35

9.0775

5

1.5

1.65

6.3775

6

1.8

1.95

3.4975

7

2.1

2.25

0.4375

8

2.4

2.55

-2.8025

9

2.7

2.85

-6.2225

10

3

   
   

Sum

51.9975

   

Total Distance(sum*h)

15.59925

 

Average Acceleration:

Using the Simpson rule and taking 10 point intervals we have the following values:

 

Interval length(0.3)

Velocity

Ordinate points

 

1

0.3

17.11

8.555

8.555

2

0.6

15.04

15.04

60.16

3

0.9

12.79

12.79

25.58

4

1.2

10.36

10.36

41.44

5

1.5

7.75

7.75

15.5

6

1.8

4.96

4.96

19.84

7

2.1

1.99

1.99

3.98

8

2.4

-1.16

-1.16

-4.64

9

2.7

-4.49

-4.49

-8.98

10

3

-8

-4

-4

     

Sum

157.435

     

Distance(sum*h/3)

15.7435

 

Average Acceleration:

The calculus method:

Average Acceleration:

For the calculus method gives the correct result the number of points taken should be more to achieve the result closer to calculus values. The Simpson’s value is the most closer. The technologies like spreadsheet hep in calculating more points and hence help in achieving the values closer to the actual.

Appendix

 

V1

V2

R

0

121.2436

-100

21.24356

0.01

121.9375

-99.995

21.94248

0.02

122.6192

-99.98

22.63921

0.03

123.2887

-99.955

23.33368

0.04

123.9458

-99.92

24.02582

0.05

124.5906

-99.875

24.71555

0.06

125.2229

-99.8201

25.40281

0.07

125.8426

-99.7551

26.08753

0.08

126.4498

-99.6802

26.76964

0.09

127.0443

-99.5953

27.44908

0.1

127.6262

-99.5004

28.12577

0.11

128.1953

-99.3956

28.79964

0.12

128.7515

-99.2809

29.47064

0.13

129.2949

-99.1562

30.13869

0.14

129.8253

-99.0216

30.80373

0.15

130.3428

-98.8771

31.46568

0.16

130.8472

-98.7227

32.12449

0.17

131.3386

-98.5585

32.78009

0.18

131.8168

-98.3844

33.43241

0.19

132.2818

-98.2004

34.08139

0.2

132.7336

-98.0067

34.72695

0.21

133.1721

-97.8031

35.36905

0.22

133.5974

-97.5897

36.00761

0.23

134.0092

-97.3666

36.64256

0.24

134.4077

-97.1338

37.27386

0.25

134.7927

-96.8912

37.90142

0.26

135.1642

-96.639

38.5252

0.27

135.5222

-96.3771

39.14512

0.28

135.8667

-96.1055

39.76113

0.29

136.1976

-95.8244

40.37316

0.3

136.5148

-95.5336

40.98116

0.31

136.8184

-95.2334

41.58506

0.32

137.1083

-94.9235

42.1848

0.33

137.3846

-94.6042

42.78032

0.34

137.647

-94.2755

43.37156

0.35

137.8957

-93.9373

43.95846

0.36

138.1307

-93.5897

44.54097

0.37

138.3518

-93.2327

45.11903

0.38

138.559

-92.8665

45.69257

0.39

138.7525

-92.4909

46.26155

0.4

138.932

-92.1061

46.8259

0.41

139.0976

-91.7121

47.38556

0.42

139.2494

-91.3089

47.94049

0.43

139.3872

-90.8966

48.49062

0.44

139.5111

-90.4752

49.03591

0.45

139.621

-90.0447

49.57629

0.46

139.717

-89.6052

50.11171

0.47

139.799

-89.1568

50.64212

0.48

139.867

-88.6995

51.16747

0.49

139.921

-88.2333

51.6877

0.5

139.961

-87.7583

52.20276

0.51

139.9871

-87.2745

52.7126

0.52

139.9991

-86.7819

53.21718

0.53

139.9971

-86.2807

53.71642

0.54

139.9812

-85.7709

54.2103

0.55

139.9512

-85.2525

54.69876

0.56

139.9073

-84.7255

55.18175

0.57

139.8493

-84.1901

55.65921

0.58

139.7774

-83.6463

56.13112

0.59

139.6915

-83.0941

56.59741

0.6

139.5916

-82.5336

57.05804

0.61

139.4778

-81.9648

57.51296

0.62

139.35

-81.3878

57.96213

0.63

139.2083

-80.8028

58.40551

0.64

139.0526

-80.2096

58.84305

0.65

138.8831

-79.6084

59.2747

0.66

138.6996

-78.9992

59.70042

0.67

138.5023

-78.3822

60.12018

0.68

138.2912

-77.7573

60.53392

0.69

138.0662

-77.1246

60.94161

0.7

137.8274

-76.4842

61.34321

0.71

137.5749

-75.8362

61.73867

0.72

137.3085

-75.1806

62.12795

0.73

137.0285

-74.5174

62.51103

0.74

136.7347

-73.8469

62.88785

0.75

136.4273

-73.1689

63.25839

0.76

136.1062

-72.4836

63.6226

0.77

135.7715

-71.7911

63.98044

0.78

135.4232

-71.0914

64.33189

0.79

135.0614

-70.3845

64.67691

0.8

134.6861

-69.6707

65.01545

0.81

134.2973

-68.9498

65.3475

0.82

133.8951

-68.2221

65.67301

0.83

133.4795

-67.4876

65.99196

0.84

133.0506

-66.7463

66.3043

0.85

132.6083

-65.9983

66.61002

0.86

132.1528

-65.2437

66.90907

0.87

131.6841

-64.4827

67.20143

0.88

131.2022

-63.7151

67.48708

0.89

130.7072

-62.9412

67.76597

0.9

130.1991

-62.161

68.03809

0.91

129.678

-61.3746

68.3034

0.92

129.1439

-60.582

68.56189

0.93

128.5969

-59.7834

68.81352

0.94

128.0371

-58.9788

69.05826

0.95

127.4644

-58.1683

69.2961

0.96

126.879

-57.352

69.52701

0.97

126.2809

-56.53

69.75097

0.98

125.6702

-55.7023

69.96796

0.99

125.0469

-54.869

70.17794

1

124.4111

-54.0302

70.38091

1.01

123.7629

-53.1861

70.57684

1.02

123.1023

-52.3366

70.76572

1.03

122.4294

-51.4819

70.94751

1.04

121.7442

-50.622

71.12221

1.05

121.0469

-49.7571

71.2898

1.06

120.3375

-48.8872

71.45027

1.07

119.616

-48.0124

71.60358

1.08

118.8826

-47.1328

71.74974

1.09

118.1373

-46.2485

71.88872

1.1

117.3801

-45.3596

72.02051

1.11

116.6113

-44.4662

72.1451

1.12

115.8307

-43.5682

72.26248

1.13

115.0386

-42.666

72.37263

1.14

114.235

-41.7595

72.47554

1.15

113.4199

-40.8487

72.5712

1.16

112.5936

-39.934

72.65961

1.17

111.7559

-39.0152

72.74075

1.18

110.9071

-38.0925

72.81462

1.19

110.0472

-37.166

72.88121

1.2

109.1763

-36.2358

72.9405

1.21

108.2944

-35.3019

72.99251

1.22

107.4018

-34.3646

73.03721

1.23

106.4984

-33.4238

73.07461

1.24

105.5843

-32.4796

73.10471

1.25

104.6597

-31.5322

73.12749

1.26

103.7247

-30.5817

73.14296

1.27

102.7792

-29.6281

73.15112

1.28

101.8235

-28.6715

73.15196

1.29

100.8576

-27.7121

73.14549

1.3

99.88158

-26.7499

73.1317

1.31

98.8956

-25.785

73.1106

1.32

97.89973

-24.8175

73.08219

1.33

96.89407

-23.8476

73.04647

1.34

95.87872

-22.8753

73.00344

1.35

94.85378

-21.9007

72.95312

1.36

93.81936

-20.9239

72.8955

1.37

92.77556

-19.945

72.83059

1.38

91.72248

-18.9641

72.75839

1.39

90.66022

-17.9813

72.67892

1.4

89.5889

-16.9967

72.59219

1.41

88.50862

-16.0104

72.49819

1.42

87.41949

-15.0225

72.39695

1.43

86.32162

-14.0332

72.28846

1.44

85.21512

-13.0424

72.17275

1.45

84.10009

-12.0503

72.04982

1.46

82.97666

-11.057

71.91968

1.47

81.84493

-10.0626

71.78235

1.48

80.70501

-9.06716

71.63785

1.49

79.55702

-8.07084

71.48618

1.5

78.40108

-7.07372

71.32736

1.51

77.2373

-6.07589

71.16141

1.52

76.06579

-5.07745

70.98834

1.53

74.88668

-4.0785

70.80817

1.54

73.70007

-3.07915

70.62093

1.55

72.5061

-2.07948

70.42662

1.56

71.30488

-1.07961

70.22527

1.57

70.09653

-0.07963

70.01689

1.58

68.88116

0.920354

69.80152

1.59

67.65891

1.920249

69.57916

1.6

66.4299

2.919952

69.34985

1.61

65.19424

3.919363

69.1136

1.62

63.95206

4.918382

68.87044

1.63

62.70349

5.916909

68.6204

1.64

61.44864

6.914845

68.36349

1.65

60.18765

7.912089

68.09974

1.66

58.92065

8.908542

67.82919

1.67

57.64775

9.904104

67.55185

1.68

56.36908

10.89868

67.26776

1.69

55.08478

11.89216

66.97694

1.7

53.79497

12.88445

66.67942

1.71

52.49978

13.87545

66.37524

1.72

51.19934

14.86507

66.06441

1.73

49.89379

15.8532

65.74699

1.74

48.58324

16.83974

65.42298

1.75

47.26783

17.82461

65.09244

1.76

45.9477

18.80768

64.75538

1.77

44.62297

19.78888

64.41185

1.78

43.29378

20.7681

64.06188

1.79

41.96026

21.74524

63.7055

1.8

40.62254

22.72021

63.34275

1.81

39.28077

23.6929

62.97367

1.82

37.93506

24.66323

62.59829

1.83

36.58556

25.63109

62.21665

1.84

35.2324

26.59639

61.82879

1.85

33.87572

27.55902

61.43475

1.86

32.51565

28.51891

61.03456

1.87

31.15233

29.47594

60.62827

1.88

29.7859

30.43002

60.21592

1.89

28.41648

31.38106

59.79754

1.9

27.04423

32.32896

59.37319

1.91

25.66927

33.27362

58.94289

1.92

24.29174

34.21497

58.50671

1.93

22.91179

35.15288

58.06467

1.94

21.52954

36.08729

57.61683

1.95

20.14514

37.01808

57.16322

1.96

18.75872

37.94518

56.7039

1.97

17.37043

38.86848

56.23891

1.98

15.98041

39.78789

55.76829

1.99

14.58878

40.70332

55.2921

2

13.1957

41.61468

54.81038

2.01

11.80129

42.52189

54.32318

2.02

10.40571

43.42483

53.83054

2.03

9.009085

44.32344

53.33253

2.04

7.611559

45.21762

52.82918

2.05

6.213273

46.10727

52.32054

2.06

4.814365

46.99231

51.80668

2.07

3.414976

47.87265

51.28763

2.08

2.015245

48.74821

50.76345

2.09

0.615312

49.61889

50.2342

2.1

-0.78468

50.48461

49.69993

2.11

-2.1846

51.34528

49.16068

2.12

-3.58429

52.20082

48.61652

2.13

-4.98363

53.05113

48.0675

2.14

-6.38247

53.89614

47.51367

2.15

-7.78067

54.73577

46.95509

2.16

-9.1781

55.56991

46.39182

2.17

-10.5746

56.39851

45.8239

2.18

-11.9701

57.22146

45.2514

2.19

-13.3643

58.03869

44.67438

2.2

-14.7572

58.85011

44.09289

2.21

-16.1487

59.65565

43.50699

2.22

-17.5385

60.45523

42.91674

2.23

-18.9266

61.24876

42.3222

2.24

-20.3127

62.03616

41.72343

2.25

-21.6969

62.81736

41.12048

2.26

-23.0789

63.59228

40.51342

2.27

-24.4585

64.36084

39.90231

2.28

-25.8358

65.12297

39.28722

2.29

-27.2104

65.87858

38.66819

2.3

-28.5823

66.6276

38.04529

2.31

-29.9514

67.36996

37.41859

2.32

-31.3174

68.10559

36.78815

2.33

-32.6804

68.8344

36.15403

2.34

-34.04

69.55633

35.5163

2.35

-35.3963

70.27131

34.87501

2.36

-36.749

70.97926

34.23024

2.37

-38.0981

71.68011

33.58204

2.38

-39.4433

72.37379

32.93048

2.39

-40.7846

73.06023

32.27563

2.4

-42.1218

73.73937

31.61756

2.41

-43.4548

74.41114

30.95632

2.42

-44.7835

75.07546

30.29199

2.43

-46.1077

75.73228

29.62462

2.44

-47.4272

76.38152

28.9543

2.45

-48.742

77.02313

28.28108

2.46

-50.052

77.65703

27.60503

2.47

-51.3569

78.28317

26.92622

2.48

-52.6568

78.90147

26.24472

2.49

-53.9513

79.51189

25.56059

2.5

-55.2405

80.11436

24.87391

2.51

-56.5241

80.70882

24.18474

2.52

-57.8021

81.2952

23.49315

2.53

-59.0742

81.87346

22.79922

2.54

-60.3405

82.44353

22.103

2.55

-61.6008

83.00535

21.40457

2.56

-62.8549

83.55888

20.704

2.57

-64.1027

84.10405

20.00136

2.58

-65.3441

84.6408

19.29673

2.59

-66.5789

85.1691

18.59016

2.6

-67.8071

85.68888

17.88173

2.61

-69.0286

86.20008

17.17152

2.62

-70.2431

86.70267

16.45958

2.63

-71.4506

87.19659

15.74601

2.64

-72.6509

87.68179

15.03085

2.65

-73.844

88.15822

14.3142

2.66

-75.0297

88.62583

13.59611

2.67

-76.2079

89.08459

12.87666

2.68

-77.3785

89.53443

12.15593

2.69

-78.5413

89.97532

11.43398

2.7

-79.6963

90.40721

10.71088

2.71

-80.8433

90.83007

9.986719

2.72

-81.9823

91.24384

9.261556

2.73

-83.113

91.64848

8.535466

2.74

-84.2354

92.04396

7.808523

2.75

-85.3494

92.43024

7.0808

2.76

-86.4549

92.80727

6.352368

2.77

-87.5517

93.17502

5.623301

2.78

-88.6398

93.53346

4.893671

2.79

-89.719

93.88254

4.163552

2.8

-90.7892

94.22223

3.433017

2.81

-91.8504

94.55251

2.702138

2.82

-92.9023

94.87332

1.97099

2.83

-93.945

95.18465

1.239644

2.84

-94.9783

95.48646

0.508174

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112.5617

-99.3601

13.20156

6.18

113.3885

-99.4681

13.9204

6.19

114.204

-99.5661

14.63785

6.2

115.008

-99.6542

15.35384

6.21

115.8006

-99.7323

16.06829

6.22

116.5816

-99.8004

16.78114

6.23

117.3509

-99.8586

17.4923

6.24

118.1085

-99.9068

18.20172

6.25

118.8543

-99.9449

18.90932

6.26

119.5881

-99.9731

19.61502

6.27

120.3101

-99.9913

20.31877

6.28

121.02

-99.9995

21.02048

6.29

121.7178

-99.9977

21.72009

6.3

122.4034

-99.9859

22.41753

6.31

123.0768

-99.9641

23.11272

6.32

123.7379

-99.9322

23.80561

6.33

124.3866

-99.8904

24.49611

6.34

125.0228

-99.8386

25.18417

6.35

125.6466

-99.7769

25.86971

6.36

126.2578

-99.7051

26.55266

6.37

126.8563

-99.6234

27.23295

6.38

127.4422

-99.5317

27.91052

6.39

128.0154

-99.4301

28.5853

 

 
OR

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